Possible to do this with Verizon?

Sorry if this has been asked before. Wasn't really sure how to word it so I didn't know how to search for it. Anyway, I'm wondering if it's possible to switch numbers between two phones with Verizon. I have an iPhone 4 and my mom has a really old piece of junk. Her contract is almost up so she can get a new iPhone 5 for $199 if she renews it. She was planning on sticking with her old phone but I told her I'd pay the $199 for the iPhone 5 and then she could swap phones with me (I give her my iPhone 4 and she gives me the iPhone 5). I'm just wondering if Verizon will let you do this. Thanks

 

Thanks, I appreciate the info.